The Mobilities of Ions

 

At infinite dilution all the ions that can arise from the electrolyte will take part in conducting the current. Thus, all solutions that contain 1 g equivalent of different electrolytes will contain the equivalent number of ions. i.e. the total charge carried by the ions will be the same for all solutions. The conductance of a solution and, thus, the quantity of electricity that can pass through it, depends the product of the number of ions, the velocity of the ions and the charge carried by each ion. Since the total charge remains the same in each case at infinite dilution, the equivalent conductance of an electrolyte will only depends on the speed of the ions. Consequently it is the different speeds of the ions that determines the conductance at infinite dilution ().

 

If the velocities of the cation and anion are (u) and (v) respectively, under a potential gradient of 1 volt per cm. Then ()  must be proportional to the sum of the speeds of the two ions, consequently.

 

 

                where (k) is a constant for all electrolytes.

 

As, () represents the contribution of the cation and () the contribution of the anion to the total conductance then

 

 

where () and () are the cation and anion conductivities respectively.

 

Consequently, the ionic conductivities are proportional to the speeds of the ions.

 

Electrophoretic separations are based on mobility diversity between differently charged species which, in turn, will depend on the charge on the molecule that will be controlled by the pH of the transport medium.